...beware of mathematicians, and all those who make empty prophecies.
The danger already exists that the mathematicians have made a covenant with the
devil to darken the spirit and to confine man in the bonds of Hell.
St. Augustine, De Genesi ad Litteram libri duodecim. Liber Secundus, 17, 37.

A review (in French)
appeared on the Gazette of Mathématiciens, 110, October 2006.

This book offers the first comprehensive treatment of the problem
of predicting "individual sequences". Unlike standard statistical
approaches to forecasting, prediction of individual sequences does
not impose any probabilistic assumption on the data-generating
mechanism. Yet, prediction algorithms can be constructed that work
well for all possible sequences, in the sense that their performance
is always nearly as good as the best forecasting strategy in a given
reference class.
The central theme is the model of "prediction using expert advice",
a general framework within which many related problems can be cast
and discussed. Repeated game playing, adaptive data compression,
sequential investment in the stock market, sequential pattern analysis,
and several other problems are viewed as instances of the experts'
framework and analyzed from a common nonstochastic standpoint that
often reveals new and intriguing connections. Old and new forecasting
methods are described in a mathematically precise way with the purpose
of characterizing their theoretical limitations and possibilities.